# Project Guidelines

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```					Project 2-Guidelines
Recall- Class Project-Goals

 Determine what would be expected to happen if each
company bid the same amount as its signal.
 Determine the Company 1 bid under several
uniform bidding strategies, and explore the expected
values of these plans.
 Find a stable uniform bidding strategy that could be
followed by all companies, without any chance for
improvement.
Recall-Project Assumptions
Assumption 1.
The same 18 companies
will each bid on future similar leases
only bidders for the tracts.
Assumption 2.
The geologists employed by companies
equally expert
on average, they can estimate the correct
values of leases.
each signal for the value of an undeveloped tract is
an observation of a continuous random variable, Sv,

Mean of Sv  v ( actual value of lease )
Recall-Project Assumptions
Assumption 3. Except for their means, the
distributions of the Sv’s are all identical

Assumption 4.
All of the companies have the same profit margins
Strategies for bidding on an Oil
Lease
• Strategy 1
-Bid your signal. What will happen? Give reasoning for your
analysis
• Strategy 2(First Plan)
-Subtract Winner’s curse from your signal to obtain bid.
Assume all other companies do the same process. What
will happen? Give reasoning for your analysis
• Strategy 3(Second Plan)
-Subtract Winner’s curse and Winner’s blessing from your
signal to obtain bid. Assume all other companies do the
same process. What will happen? Give reasoning for
Strategies for bidding on an Oil
Lease
• Strategy 4
-Find a optimal adjustment for company 1. Assume all
other companies Subtract Winner’s curse and Winner’s
blessing from their signals to obtain their bids.
• Strategy 5
-Find a optimal adjustment for company 1. Assume all
other companies Subtract Winner’s curse from their
signals to obtain their bids.

• Strategy 6
-Determine a stable Nash equilibrium bid. This stable
strategy is such that any company will not have any
incentive to deviate from
Strategy 1
-Bid your signal. What will happen? Give reasoning for your
analysis

•  The company (highest signal) will submit the highest bid-> win the
lease.
• Under this plan, our company would submit a bid of its signal, s1 =
\$121,600,000
• “Winner’s Extra Profit” is almost always negative. That is, the winning
company will not get its needed fair return on the lease.
• The mean of the 18 signals for a new lease = the actual value of the
lease.Because for example, historical auction 1 the mean lease
signal=85.3 M & proven value =91M
(Assumption 2)

•    Hence, the highest signal will almost always be well above the value
of the lease and the winning company will have paid too much for the
drilling rights. This is called the winner’s curse.

•   WC=avg of the maximum error column
Strategy 2(First Plan)
-Subtract Winner’s curse from your signal to obtain bid.
Assume all other companies do the same process. What
will happen? Give reasoning for your analysis
• defeat the winner’s curse.
• estimate the expected size of the curse
• Let C be the continuous random variable which gives the largest
number in a sample of 18 observations of R(error).
• E(C)=winner’s curse=avg. of the maximum error column
• If a company bids its signal and wins the auction, it can expect,
on average, to fall \$22,600,000 below its needed fair return on
the lease.
• If each company bids 22.6 million dollars less than its signal,
then any one of the companies is equally likely to win the
auction, and there will be no winner’s curse.
• Under this plan, our company would submit a bid of 121.6  22.6
million dollars, that is \$99,000,000
Strategy 3(Second Plan)
-Subtract Winner’s curse and Winner’s blessing from your signal to
obtain bid. Assume all other companies do the same process. What will
happen? Give reasoning for your analysis

• In an auction where the highest bid wins, any amount that the
winner pays above the second highest bid is wasted.
• Let B be the continuous random variable which gives the difference
between the largest and second largest errors in a random set of 18
observations of R.

• E(B)=winners blessing=average of the difference column=5.8M
• the winning company will, on average, pay an unnecessary premium
of 5.8 million.
• This leads to another possible bidding strategy, that we will call the
Second Plan.
• Each company could bid \$22,600,000 + \$5,800,000 =
\$28,400,000 less than its signal.
• Under this plan, our company would submit a bid of 121.6  28.4
million dollars, that is 93.2M
Bidding on
Probability, Mathematics, Tests, Homework, Computers
The larger the expected value of Company 1’sOil Leasethe
better is the long term effect of that bidding plan for us.
on the project
reduce by both the winner’s curse and blessing for Company 1 and
all other companies.

each company has approximately the same chance of winning, and, if a
company wins, it can expect an extra profit that is close to the 5.8 million
dollar winner’s blessing.                       Results Of Adjustment
Average
For All
Other
Company 1 Companies
Probability of Winning        0.057          0.055
Mean Extra Profit If Company Wins           5.843          5.832
Expected Value Of Adjustment            0.335          0.323

Auction Focus.xls
Simulating, Focus    Class Project     (material continues)             T    C     I    
Strategy 4
-Find a optimal adjustment for company 1. Assume all
other companies Subtract Winner’s curse and Winner’s
blessing from their signals to obtain their bids       .
• steps
• 1. Enter the sum of the WC & WB as the signal adjustment for all
other companies cell
• 2. Change company 1 signal adjustment cell to get a set of
expected values for company 1.
• 3. record results of expected value for company 1
• How to find good adjustment points(10 points ) for company1?
• For example, If your WC=23,you could use 25,27,29,31,33
• and 21,19,17,15
• 4. enter each good adj. ->hit F9(to recalculate)->manually record
the expected values & create a table for company 1
Strategy 4-
Bidding on
Probability, Mathematics, Tests, Homework, Computers
Constructing      f(a) function Leasean Oil
on the project
Company 1
for Company 1 must
find the maximum              Subtract
Expected Value
expected value of                13             0.245
that all other                   17             0.505
companies subtract               19             0.507
21             0.511
both the curse and
23             0.491
blessing)                        25             0.426
acb                              29             0.327
31             0.237
Strategy 4
f(a) function
COMPANY 1: CURSE & BLESSING FOR ALL OTHERS
0.6
0.5
Expected Value

0.4
0.3
0.2
0.1
0.0
0   2   4   6   8 10 12 14 16 18 20 22 24 26 28 30 32
copy from the sheet Strategy in Auction Focus.xls.
 Let f(a) be the expected value for Company 1 for subtracting a million
dollars from its signal, assuming that all other companies adjust their signals
by both the curse and blessing.
Fit a 4th degree polynomial trend line, which we will use as an approximate
Computation
formula for the unknown function f.            a     f (a )   f '(a )
Use solver to find the best adjustment 18.9166 0.524 0.000
Strategy 4
• This is the real world of business,competitors
may also elect to subtract less than 28.4 million
dollars from their signals.
•     there is a strong incentive for individual
companies to deviate from the strategy and
subtract less than the curse and blessing.
•     Company 1’s best adj. 18.9166 million is
not itself a stable strategy.
Strategy 5
-Find a optimal adjustment for company 1. Assume all
other companies Subtract Winner’s curse from their
signals to obtain their bids    .
• steps
• 1. Enter the WC as the signal adjustment for all other companies
cell
• 2. Change company 1 signal adjustment cell to get a set of
expected values for company 1.
• 3. record results of expected value for company 1
• How to find good adjustment points(10 points ) for company1?
• For example,If your WC=23,you could use 25,27,29,31,33
• and 21,19,17,15
• 4. enter each good adj. ->hit F9(to recalculate)->manually record
the expected values & create a table for company 1
Strategy 5           Bidding on
Probability, Mathematics,   Tests, Homework, Computers
an Oil Lease
Constructing g(a) function
on the project
Company 1
for Company 1 must                Signal Adjustment:
Expected Value
find the maximum                       Subtract
expected value of                         17             -0.190
19             -0.106
21             -0.036
that all other                            23             0.007
companies subtract                        25             0.020
both the curse and                        27             0.033
blessing)                                 29             0.029
33             0.018
ac
35             0.011
37             0.007
Auction Focus.xls
Simulating, Focus   Class Project                                     T      C     I     
(material continues)
Strategy 5
g(a) function
COMPANY 1: CURSE ONLY FOR ALL OTHERS
0.1
0.1
Expected Value

0.0

-0.1 0   5    10    15    20    25     30   35   40

-0.1
-0.2
-0.2

USE the sheet Strategy in Auction Focus.xls.
 Let g(a) be the expected value for Company 1 for subtracting a million dollars from its signal,
assuming that all other companies adjust their signals by curse.
Fit a 4th degree polynomial trend line, which we will use as an approximate formula for the
unknown function g.
Use solver to find the best adjustment
the use of Solver in Strategy shows that g(27.5990) = 0. Hence, ac = 27.5990 million
dollars.
Company 1’s best response to an adjustment of 22.6 million dollars by all
other companies is to lower its signal by the considerably larger amount of \$27,599,000.
Strategy 5
if we know what all other companies plan to
do. Moreover, this same information is available
to all of the bidders.
Need a stable strategy???
If all companies made such a stable
adjustment to their signals, then there would
be no incentive for anyone to alter the
strategy. A stable bidding strategy is also called
a Nash equilibrium
Strategy 6
How?
(a) Use Auction Equilibrium.xls(.
(b) FOLLOW THE INSTRUCTIONS IN THIS FILE!
(c) Enter appropriate values in cells B10 through E10.
(d) Enter a logical value in cell E39. Run the macro Optimize.
(the first logical value to use- (2wc+wb)/2
(e) Enter another logical value in cell E39 and press the key F9..
record numbers in a table.
(f)    See table
(g) Find the stable adj for strategy 6
first logical value to
use for class

Strategy 6                 project-
(2wc+wb)/2=25.5
Company 1           All Other     New logical value
Optimal             Companies
(use 4 decimals)    Subtracted
From Signal

1                                      (25+22.5414)/2=23.770
22.5414             25.5
7
2
23.7707
.

.

10

Avg of amax=final
strategy 6
Extra Profit
• Extra profit is the amount by which the winning
bid is below the fair value of a lease.
• Let Xi be the random variable giving the extra
profit gained by Company i. The sample of
10,000 simulated auctions is used to
approximate E(X1) and the average of E(X2),
E(X3), ..., and E(X18)                  Results Of Adjustment
Average
Extra profit of winning company                                                   For All
Other
Company 1        Other Companies
Company 1 Companies
-2.0
-11.0                                  Probability of Winning   0.123     0.052
0.2   Mean Extra Profit If Company Wins    4.203     5.487
-3.7       Expected Value Of Adjustment     0.517     0.283

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 views: 3 posted: 9/7/2011 language: English pages: 22